Abstract:

If T is an isomorphism of (c₀) into C(\Omega) (where \Omega is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||●||T^-1||≤1+ε for some ε∈ (0, 1/5), then T /||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.

Key words: Small into isomorphism, isometry, almost isometry